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  • If the coefficient of second, third and fourth terms in the expansion of 1 plus x exponent of 2 are in A.P., then show that 2n e

 If the coefficient of second, third and fourth terms in the expansion of (1+x)2n  are in A.P., then show that 2n2 – 9n + 7 = 0.

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Coefficient of (r+1)th in the expansion of (1+x)2n is 2nCr
Given 2nd, 3rd and 4th terms are in A.P
⇒2.2nC2=2nC1+2nC3
⇒2n(2n−1)=2n+\frac{2n(2n-1)(2n-2)}{6}
⇒6(2n−1)=6+4n2−6n+2
⇒2n2−9n+7=0

 

Posted by

Satyajeet Kumar

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